I won't get into a flame war with anyone over this, but I'll answer your question. Teens are considered adults (and as such, are not required to notify or obtain consent from a parent) when it comes to three and only three things in medicine: mental health, treatment for drug and alcohol abuse, and all things sexual health. This includes obtaining birth control, treatment for STDs, and yes, making decisions regarding what to do with an unplanned pregnancy. No one's debating the first two on this list; why attack the third?
The majority of teens already involve a parent when they decide to terminate a pregnancy. Those who do not are far, far more likely to cite fear of abuse (psychological or physical) or fear of being kicked out of the house as reasons why they don't wish to tell a parent. If we were to pass a law stating that these young women have to tell an abusive parent that they're pregnant and wish to have an abortion, we run the risk that these women will resort to alternative measures.
In other states with parental notification or consent laws, such as Massachussets, Missouri, and Mississippi, the in-state teen abortion rate declined, but the teen abortion rate in neighboring states rose by nearly the same amount. It's not that teens aren't getting abortions, it's that they're waiting longer (indeed, there are more second-trimester abortions taking place in surrounding states than there were previously) and traveling long distances to do so. This, clearly, is more dangerous, and is NOT a desirable outcome. Further, there are fears that teenagers who are unable to travel out of state to obtain an abortion but feel that they cannot have a baby will resort to drastic measures such as attempting to self-abort. There are plenty of "instructions" on the internet for such things, and it's a valid concern.
There is a provision for judicial bypass, but it's not a particularly valid option for your average teenager. It requires a lot of knowledge about legal procedure (which I sadly do not have, and therefore can't expound upon), added time, and the decision as to whether or not a young woman can have an abortion without notifying her parents ultimately rests with the judge, who may or may not grant her that option. Some judges in other states are notoriously anti-abortion, and simply don't ever say yes to these women. And again, even if a woman is able to obtain an abortion without telling her parents, that's added time, and abortion procedures become more complicated the longer you wait.
Lastly, here in California, teen pregnancy rates have been steadily falling over the last decade, moreso than the national rates have been falling. Abortion rates have also been falling. We're clearly doing something right. The parental notification law won't help; if anything, it's going to harm the state's teens, because they're going to do what teens in other states have already done: wait longer and travel across state lines to get abortions anyway. We can't legislate good communications and relations within families. All we can do is help our patients make the best and safest decisions for themselves.
All data, claims, etc. come directly from this publication by the Center for Reproductive Health Research and Policy at UCSF:
http://crhrp.ucsf.edu/publications/files/ParentalNotification_2006Aug.pdf
I highly suggest reading it if you're interested.